GTRAN2 is a two dimension (2D) general geometry multigroup neutron transport code which combines the geometric flexibility of Monte Carlo (MC) codes with the computational efficiency of deterministic codes. Due to its geometrical flexibility, this code can be used for calculations of reactors with complex geometrical features. This code is based on the exact collision probability (CP) formalism for the solution of the integral form of the neutron transport equation. This method is considered to be very accurate, but several major limitations have prevented its broader utilization over the past three decades. Some of these limitations are briefly summarized in the following paragraphs.
Computer memory limitation. The spatial coupling of all regions in the global domain results in large and dense CP matrices. Very fine meshing is required for some problems, since the CP method gains accuracy with increasing subdivision of the regions. The number of meshes that can be treated is severely limited by the available computer memory, since the number of CP matrix elements increases as N.sub.r.sup.2 x N.sub.g, with N.sub.r being the total number of meshes, and N.sub.g being the total number of energy groups. As an example, consider a domain divided into 500 meshes. For a 12-group problem, the CP matrix will consist of 500.times.500.times.12=3.times.10.sup.6 double precision elements, requiring 24 Mbytes of memory.
Computational cost limitation. Calculation of the CP matrix is the most time-consuming part of the entire calculation in the lattice codes based on this method. Moreover, the CPU time increases rapidly with the increased mesh refinement needed to achieve high accuracy in the CP calculations. The calculation of the CP matrices can sometimes require more than 95% of the total CPU time.
Isotropic scattering limitation. With the assumption of isotropic neutron scattering and isotropic sources, integration over the angular variable in the integral transport equation can be carried out easily, and a simplified equation for the scalar flux is obtained. If linearly anisotropic scattering is assumed, the number of eigenvalue equations in 2D is increased to three and the number of large CP matrices to nine, to account for higher order flux moments. This is prohibitively expensive and no code has been developed which accounts for linearly anisotropic neutron scattering in two-dimensional geometries.
Geometry limitation. The geometrical portion of the CP calculation includes determination of the intersection points between straight lines and region boundaries, i.e., surfaces. The usual procedure was to write a different algorithm for each different geometry, resulting in lattice codes with limited applicability.
In order to remedy some of the above mentioned limitations, several related methods were developed in the early seventies, based on the so called interface-current formalism. In order to replace large and dense CP matrices with sparse matrices, regions were decoupled, usually on the pin cell level, and coupled only to the neighboring regions through interface currents. In these methods some accuracy had to be sacrificed, because some additional approximations on the pin cell interfaces had to be made.
The present invention overcomes the aforementioned limitations of the prior art by providing a method for determining neutron transport in a nuclear reactor which is more accurate than previous methods and which can be used for virtually any advanced reactor design, thus saving man-years of effort. The inventive method is also faster than the prior approaches, and thus more cost efficient, and allows for highly precise analysis of complicated and irregular nuclear reactor assemblies in one, two or three dimensions.